My Australian passport (correctly) lists my birth city as "Upper cityname" whereas my UK passport simply mentions my birth city as "cityname". Is this an error that I should care about?
If I were you, I would look into what would be required to make the change in your UK passport, the next time it comes up for renewal. Paperwork like this tends to be more convenient when properly reflecting reality.
That said, there's no major reason to think this would ever become a practical issue; the two documents are, as it were, part of disconnected administrative backbones.
I'm in the exact same circumstance as you. One even includes my middle name whereas the other does not. My birth places are
City on one and
Town on the other.
This hasn't ever been a problem in all of my travels and shouldn't be a problem to you.